Math Problem Statement
For the following linear system: x + y - z = 1, 2x + 3y + k*z = 3, x + k*y + 3z = 2. Find the value(s) of k for which the system has: (i) no solution, (ii) unique solution, (iii) infinite solutions.
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Algebra
Systems of Linear Equations
Matrices and Determinants
Formulas
Determinant of a matrix: det(A) = Σ (product of elements and their cofactors)
Condition for unique solution: det(A) ≠ 0
Condition for infinite/no solution: det(A) = 0 and rank conditions
Theorems
Cramer's Rule
Rank-Nullity Theorem
Suitable Grade Level
Grades 11-12
Related Recommendation
Solving a System of Linear Equations with Parameters m and k
Finding k for a System of Equations with Augmented Matrix in Row-Echelon Form
Infinitely Many Solutions: Solving Linear Equations with Parameter k
Solving a System of Linear Equations Using Matrix Inverses: x1 + 4x2, x2 + x3, 3x1 - x2 - 14x3
Solve Homogeneous System of Equations with Determinant Condition